Probing AGB nucleosynthesis via accurate Planetary Nebula ... · 70 CHAPTER 5: Probing AGB nucleosynthesis via accurate Planetary Nebula abundances 5.1 Introduction Planetary Nebulae

5Probing AGB nucleosynthesis via

accurate Planetary Nebulaabundances

Based on:P. Marigo, J. Bernard-Salas, S.R. Pottasch, A.G.G.M. Tielens, & P.R. Wesselius

ASTRONOMY & ASTROPHYSICS, IN PRESS (2003)

THE elemental abundances of ten planetary nebulae, derived with high accuracy includingISO and IUE spectra, are analysed with the aid of synthetic evolutionary models for the

TP-AGB phase. The accuracy on the observed abundances is essential in order to make areliable comparison with the models. The advantages of the infrared spectra in achieving thisaccuracy are discussed. Model prescriptions are varied until we achieve the simultaneousreproduction of all elemental features, which allows placing important constraints on thecharacteristic masses and nucleosynthetic processes experienced by the stellar progenitors.First of all, it is possible to separate the sample into two groups of PNe, one indicating theoccurrence of only the third dredge-up during the TP-AGB phase, and the other showingalso the chemical signature of hot-bottom burning. The former group is reproduced by stellarmodels with variable molecular opacities (see Marigo 2002), adopting initial solar metallicity,and typical efficiency of the third dredge-up, λ ∼ 0.3 − 0.4. The latter group of PNe, withextremely high He content (0.15 ≤He/H≤ 0.20) and marked oxygen deficiency, is consistentwith original sub-solar metallicity (i.e. LMC composition). Moreover, we are able to explainquantitatively both the N/H–He/H correlation and the N/H–C/H anti-correlation, thus solvingthe discrepancy pointed out long ago by Becker & Iben (1980). This is obtained only underthe hypothesis that intermediate-mass TP-AGB progenitors (M & 4.5− 5.0M�) with LMCcomposition have suffered a number of very efficient, carbon-poor, dredge-up events. Finally,the neon abundances of the He-rich PNe can be recovered by invoking a significant productionof 22Ne during thermal pulses, which would imply a reduced role of the 22Ne(α, n)25Mgreaction as neutron source to the s-process nucleosynthesis in these stars.

70 CHAPTER 5: Probing AGB nucleosynthesis via accurate Planetary Nebula abundances

5.1 Introduction

Planetary Nebulae (PNe) are assumed to consist of the gas ejected via stellar winds bylow- and intermediate-mass stars (having initial masses 0.9 ≤ M/M� ≤ Mup, withMup ∼ 5 − 8M� depending on model details) during their last evolutionary stages, theso-called Thermally Pulsing Asymptotic Giant Branch (TP-AGB) phase.

PNe offer potentially a good possibility to test the results of stellar nucleosynthesis. Thiscan be done in a reliable way by comparing the predicted abundances of the gas ejected closeto the end of the AGB phase with the observed abundances because the expelled hot gas re-mains unaffected by interaction with the ISM or with previous shell ejection. Furthermore theionized gas surrounding the central star shows lines of many elements from which accurateabundances can be derived. Also by the ejection of the outer layers PNe contribute to theenrichment of the interstellar medium (ISM) and therefore, a knowledge of these processesis essential to better understand the chemical composition of the Galaxy.

PN elemental abundances represent the cumulative record of all nucleosynthetic andmixing processes that may have changed the original composition of the gas since the epochof stellar formation. In fact, stellar evolution models predict the occurrence of severalepisodes in which the envelope chemical composition is altered by mixing with nuclearproducts synthesised in inner regions and brought up to the surface by convective motions(e.g. Iben & Renzini 1983; Forestini & Charbonnel 1997; Girardi et al. 2000). Thesedredge-up events usually take place when a star reaches its Hayashi line and develops anextended convective envelope, either during the ascent on the Red Giant Branch (RGB; thefirst dredge-up), or later on the early AGB (the second dredge-up). Then, the subsequentTP-AGB evolution is characterised by a rich nucleosynthesis whose products may berecurrently exposed to the surface synchronised with thermal pulses (the third dredge-up), orconvected upward from the deepest envelope layers of the most massive stars (hot-bottomburning, hereinafter also HBB).

As a consequence, the surface abundances of several elements (e.g. H, He, C, N,O, Ne, Mg) may be significantly altered, to an extent that crucially depends on stellarparameters (i.e. mass and metallicity) various incompletely understood physical processes(e.g. convection, mass loss), and model input prescriptions (e.g. nuclear reaction rates,opacities, etc.). In this sense, the interpretation of the elemental patterns observed in PNeshould give a good insight into the evolutionary and nucleosynthetic properties of the stellarprogenitors, thus putting constraints on these processes.

For instance, the enrichment in C exhibited by some PNe should give a measure of theefficiency of the third dredge-up, still a matter of debate. Conversely, the deficiency in Cshown by some PNe with N overabundance could be interpreted as the imprint of HBB,implying rather massive TP-AGB stellar progenitors (with initial masses ≥ 4M�). The Hecontent should measure the cumulative effect produced by the first, possibly second and thirddredge-up, and HBB. The O abundance may help to constrain the chemical compositionof the convective inter-shell developed at thermal pulses, as well as the efficiency of HBB,depending on whether this element is found to be preserved, enhanced or depleted in thenebular composition. Finally, the Ne abundance in PNe could give important information

5.1. Introduction 71

about the synthesis of this element during thermal pulses, i.e. providing an indirect estimateof the efficiency of the 22Ne(α, n)25Mg reaction with important implications for theslow-neutron capture nucleosynthesis.

In this context, the present study aims at investigating the above issues by analysingaccurate determinations of elemental abundances for a sample of PNe with the aid of stellarmodels for low- and intermediate stars, that follow their evolution from the main sequenceup to the stage of PN ejection. Particular attention is paid to modelling the TP-AGB phase toderive indications on the mass range and the metallicity of the stellar progenitors involved,and the related nucleosynthetic processes, i.e. the second and third dredge-up and HBB.

An important problem when deriving PNe abundances is the correction for unseenstages of ionization. When using optical and/or UV spectra many stages of ionization aremissing and have to be inferred, making the error in the abundance determination high. Thisestimate for unobserved stages of ionization is done making use of Ionization CorrectionFactors (ICF) which are mainly derived on the basis of similarities of ionization potentials orionization models. The latter needs a very good knowledge of the stellar parameters which isoften not known. When all important stages of ionization of a certain element are measuredno ICF is needed (or ICF=1). In the past literature ICF ranging from 2-5 (and sometimes 20)are found. Many missing stages of ionization are seen in the infrared providing an importantcomplement to the UV and optical spectra. The ICF of many elements has been drasticallyreduced thanks to the inclusion of the ISO (Kessler et al. 1996) data. It has certainlyimproved the Ne, Ar, Cl and S abundances and has provided information of other importantstages of ionization such as C++, O3+ and N++. In many cases the ICF is not needed andon the others is often lower than 1.5. Another important advantage is the independence ofthe infrared lines to the adopted electron temperature. This avoids uncertainties when theelectron temperature adopted to derive the abundances is uncertain or when there are electrontemperature fluctuations in the nebula. These and other advantages have been previouslydiscussed by Beintema & Pottasch (1999) and Bernard Salas et al. (2001, chapter 2).

The paper is organised as follows. Sect. 5.2 introduces the sample of ten planetary neb-ulae, in terms of individual characteristic like: galactic coordinates, radii, nebular fluxes inH and He II recombination lines, Zanstra temperatures and luminosities of the central nuclei.These two latter parameters locate the central stars in the Hertzsprung-Russell (HR) diagram.Sect. 5.3 presents the nebular elemental abundances of He, C, N, O, Ne, S, and Ar, comparedwith the solar values, and sub-grouped as a function of helium content. Sect. 5.4 outlines asummary of the main physical processes expected to alter the surface chemical compositionof low- and intermediate-mass stars. Sect. 5.5 details the synthetic TP-AGB models adoptedfor our theoretical study, in terms of the main input parameters. The interpretative analysisof the abundance data is developed in Sect. 5.6. Finally, a recapitulation of the most relevantconclusions and implications in Sect. 5.7 closes the paper.


Table 5.1–. Parameters of the PNe. The mV is not corrected for extinction. References to distance, Vmagnitude and extinction are given by superscripts dx, mx, and ex respectively.

Name l(◦) b(◦) d (kpc) mV (mag) EB−V C/O He/HNGC 2440d1,m1,e1 234.8 2.42 1.63 17.49 0.34 > 1 0.119NGC 5315d2,m2,e2 309.1 -4.40 2.60 14.40 0.37 < 1 0.124NGC 6302d3,m3,e3 349.5 1.06 1.60 18.90: 0.88 < 1 0.170NGC 6445d1,e4,e4 8.08 3.90 2.25 19.04 0.72 < 1 0.140NGC 6537d1,m4,e5 10.10 0.74 1.95 22.40 1.22 ∼ 1 0.149NGC 6543d4,m1,e6 96.47 29.9 1.00 11.29 0.07 < 1 0.118NGC 6741d1,m5,e7 34.6 -2.28 1.65 19.26 0.75 . 1 0.111NGC 7027d5,m1,e8 84.93 -3.50 0.65 16.53 0.85 > 1 0.106NGC 7662d3,m1,e7 106.6 -17.6 0.96∗ 14.00 0.12 < 1 0.088He 2-111d1,m3,e5 315.0 -0.37 2.50 20.00: 0.77 < 1 0.185

References: d1 Average from Acker et al. (1992); d2 Liu et al. (2001); d3 Terzian (1997);d4 Reed et al. (1999); d5 Bains et al. (2003); m1 Ciardullo et al. (1999); m2 Acker et al.(1992); m3 Assumed mV ; m4 Pottasch (2000); m5 Heap et al. (1989); e1 Bernard Salas et al.(2002, chapter 3); e2 Pottasch et al. (2002); e3 Beintema & Pottasch (1999); e4 van Hoofet al. (2000); e5 Pottasch et al. (2000); e6 Bernard-Salas et al. (2003, chapter 4); e7 Pottaschet al. (2001); e8 Bernard Salas et al. (2001, chapter 1).: Large error.∗ Average distance by Terzian (1997).

5.2 Sample of PNe

5.2.1 General

The sample used is biased to bright objects, in order to measure many different stages ofionization and accurately derive their abundances. The general parameters of the PNe usedin this study are given in Table 5.1. References for the assumed distances, magnitudes andextinction are given as footnotes in the table.

Galactic coordinates show that most of these nebulae belong to the disk (exceptNGC 6543 and NGC 7662) and could be descendants of young progenitors. Distances arevery uncertain and great care was taken to adopt the most reliable ones from the literature.They vary between 0.8 and 2.5 kpc and therefore are close, as would be expected for brightobjects. There are different values in the literature that do not agree within the uncertaintiesthe authors quote. Note that the mV of He 2-111 and NGC 6302 are assumed since their cen-tral stars have never been seen. The extinction is low in most cases except for NGC 6537. Inorder to classify them according to their chemical composition the last two columns of Ta-ble 5.1 give the C/O and He/H ratios. There are two C-rich PNe, six O-rich PNe and two forwhich it is difficult to assess their nature since the C/O ratio is (although lower than one) veryclose to unity (within the uncertainties). Notice that this sample contains a higher percentageof PNe with a high He/H ratio than many other samples.

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Table 5.2–. Radius, Zanstra temperature and luminosity of the observed PNe. F(Hβ) and F(4684A) are in units of 10−12

erg cm−2 s−1 (not corrected for extinction). The radius is in meter.

Name Hydrogen Helium

F(Hβ)† Radius log( L∗

L�) log TZ(H) F(4686A)∗ Radius log( L∗

L�) log TZ(He)

NGC 2440 31.6 2.2E+07 2.95 5.25 19.3 2.1E+07 3.08 5.29NGC 5315 38.1 2.7E+08 3.34 4.80 - - - -NGC 6302: 29.5 1.7E+07 3.86 5.52 16.6 1.7E+07 3.88 5.53NGC 6445 7.60 2.4E+07 3.19 5.28 3.40 2.4E+07 3.19 5.28NGC 6537 2.20 5.8E+06 3.50 5.67 3.10 4.6E+06 4.09 5.87NGC 6543 245 3.6E+08 2.96 4.64 14.7 2.8E+08 3.46 4.82NGC 6741 4.40 1.8E+07 2.69 5.22 1.60 1.8E+07 2.69 5.22NGC 7027 75.9 2.7E+07 3.31 5.29 31.1 2.8E+07 3.27 5.28NGC 7662 102 7.8E+07 2.54 4.87 17.4 6.8E+07 2.82 4.97He 2-111: 0.98 2.5E+07 2.37 5.08 0.89 2.0E+07 2.82 5.24: Large error in the radius, temperature and luminosity.† From the same references as the extinction in Table 5.1.∗ From Acker et al. (1992).


NGC 6537

NGC 6302

NGC 7662

NGC 6543

NGC 5315

NGC 2440

NGC 6741

He 2-111

NGC 6445

NGC 7027

Figure 5.1–. HR diagram for the PNe of the sample (diamonds). The Teff have been derived with theZanstra method using the helium lines except for NGC 5315 (open diamond). The Post-AGB evolu-tionary tracks from Vassiliadis & Wood (1994) for Z=0.016 are also plotted for different core masses,indicated in the lower-right corner of the figure. In the lower-left the uncertainty in the luminosity dueto the error of a factor two in the distance is shown.

5.2.2 HR diagram

With the data in Table 5.1 and the Hβ and helium λ4686A fluxes the Zanstra temperatures(TZ), radii and luminosities have been derived (see Table 5.2). As pointed out by Stasinska &Tylenda (1986) when using the Zanstra method, TZ is over-estimated in the case of hydrogenand underestimated when using helium. This is because the Zanstra method assumes thatenergies above 54.4 eV are only absorbed by helium. This is not completely true. Inaddition recombination of He2+ sometimes produces more than one photon which can ionizehydrogen and the proportion of stellar photons with energies above 54.4 increases with Teff .Both TZ(He) and TZ(H) yield the same results for most PNe. TZ(H) fails when the nebula isthin and some photons escape. In the case of a thick nebula both methods should yield thesame result, but this is tricky because a nebula can be thick in the torus and thin in the poles.For all those reasons the TZ(He) was preferred over TZ(H).

These results are shown in Fig. 5.1. For NGC 5315 no helium line is detected so thatresults using TZ(H) have been plotted. The evolutionary tracks of Vassiliadis & Wood (1994)

5.3. Accurate abundances of ISO-observed PNe 75

Figure 5.2–. Observational abundances with respect to Solar. In the upper-left corner a typical er-ror bar for all elements except helium is plotted. The solid line represents abundances equal to solarabundances

are related to the core mass rather than the initial mass. Stars with different initial mass anddifferent mass loss functions can lead to the same core mass.

The majority of PNe are within the range of temperature and luminosity of the theoreticalevolutionary tracks. Most are in the last stage of the PNe phase. NGC 6537 lies outsideand it must be noticed that using TZ(H) makes this object closer to NGC 6302. While thisfigure may provide some insight in core mass and time evolution of these objects, the manyuncertainties (especially in distance) should be born in mind.

5.3 Accurate abundances of ISO-observed PNe

5.3.1 Abundances

Accurate abundances are needed in order to make a reliable comparison with theoreticalmodels. For this purpose a sample of ten PNe was selected in which precise abundances usingISO data have been derived. The references for the abundances are as follows: NGC 2440 →Bernard Salas et al. (2002, chapter 3); NGC 5315 → Pottasch et al. (2002); NGC 6302 →Pottasch & Beintema (1999); NGC 6445 → van Hoof et al. (2000); NGC 6537 and He 2-111→ Pottasch et al. (2000); NGC 6543 → Bernard-Salas et al. (2003, chapter 4); NGC 6741and NGC 7662 → Pottasch et al. (2001); NGC 7027 → Bernard Salas et al. (2001, chapter 2).

It should be noticed that NGC 6302, NGC 6537 and He 2-111 are among those PNe with ahot central star, a strong bipolar morphology, and in which high velocity shocks are present.

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Table 5.3–. PNe abundances\ w.r.t. hydrogen in number. The number between parenthesis (x) stands for 10x. Abun-dance reference values for the Sun, Orion, and LMC are also included.

Name Helium Carbon(-4) Nitrogen(-4) Oxygen(-4) Neon(-4) Sulfur(-5) Argon(-6)NGC 2440 0.119 7.2 4.4 3.8 1.1 0.5 3.2NGC 5315 0.124 4.4 4.6 5.2 1.6 1.2 4.6NGC 6302 0.170 0.6 2.9 2.3 2.2 0.8 6.0NGC 6445 0.140 6.0 2.4 7.4 2.0 0.8 3.8NGC 6537 0.149 1.8 4.5 1.8 1.7 1.1 4.1NGC 6543 0.118 2.5 2.3 5.5 1.9 1.3 4.2NGC 6741 0.111 6.4 2.8 6.6 1.8 1.1 4.9NGC 7027 0.106 5.2 1.5 4.1 1.0 0.9 2.3NGC 7662 0.088 3.6 0.7 4.2 0.6 0.7 2.1He 2-111 0.185 1.1 3.0 2.7 1.6 1.5 5.5Sun∗ 0.100 3.55 0.93 4.9 1.2 1.86 3.6Orion† 0.098 2.5 0.60 4.3 0.78 1.5 6.3< LMC >] 0.089 1.10 0.14 2.24 0.41 0.65 1.9\ See Sect. 5.3.1 for references.∗ Grevesse & Noels (1993) and Anders & Grevesse (1989) except the oxygen abundance which was taken fromAllende Prieto et al. (2001).† Esteban et al. (1998).] From Dopita et al. (1997).

5.3. Accurate abundances of ISO-observed PNe 77

The presence of the latter can affect the abundance composition which has been derivedassuming that the ionization is produced by the hot central star. For He 2-111 the velocity ofthe shocks have been estimated by Meaburn & Walsh (1989) to be ∼380 km/s. They show thatthese high velocity shocks are localized in the outermost parts of the bi-polar lobes (which areless dense). They conclude that photo-ionization by a hot star is the most plausible dominantprocess in the core and dense disk. Since these shocks affect the less dense regions the effectthat they might have on the abundance determination is very small and can be neglected.High velocity shocks in NGC 6302 were first presumed to be detected by Meaburn & Walsh(1980) from a study of the wings in the Ne V line at 3426 A. However, this is not supportedin more recent work by Casassus et al. (2000) using echelle spectroscopy of IR coronal ions.Even if these shocks were present, a study of Lame & Ferland (1991), in which they fitphoto-ionization models to their spectrum, indicate that only very high stages of ionization,such as Si6+ (IP 167 eV), are produced by shocks. These high stages of ionization havenegligible weight on the overall abundance which is therefore not affected by the presenceof the shocks. The speed of the shocks in NGC 6537 is ∼ 300 km/s (Corradi & Schwarz1993). Hyung (1999) studied this specific problem of the source of the nebular emissionarising either by the hot central star or by shock heating, with the help of photo-ionizationmodels. He concludes that the radiation of the hot central star is responsible for the emission.In summary, the high velocity shocks present in these PNe do not play a role in the abundancedetermination.

It should be noticed as well, that the UV flux from the hot central stars (see Table 5.2) inthese three nebulae produces a high degree of ionization. In fact, Si5+ and Si6+ have beenmeasured in both NGC 6302 and NGC 6537 (Beintema & Pottasch 1999; Casassus et al.2000), and in NGC 6302 even Si8+ and Mg7+ that require very high ionization potentials.The oxygen abundance measured in these nebulae by Pottasch et al. (2000); Pottasch &Beintema (1999) account for oxygen up to O3+ and it may be that the ICF adopted forthese nebulae (∼1.3) could be underestimating species such as O4+, O5+, O6+. The sameargument applies to the carbon abundance. Nonetheless, the ionic abundance of O2+ isalways larger (approximately a factor 2) than the contribution of O3+. Thus, one wouldexpect that the ionic abundances of higher stages of ionization are smaller. In fact, the ionicdistribution of neon abundance in these nebulae, peaks at Ne++ for NGC 6302 and He 2-111,and at Ne3+ for NGC 6537, decreasing dramatically with higher stages of ionization (Ne4+

and Ne5+). The IP of Ne4+ and Ne5+ are 97.1 and 126.2 eV respectively, and that of O4+

113.9 eV. We therefore do not think that the ICF used by Pottasch et al. (2000); Pottasch& Beintema (1999) for the determination of the oxygen abundance in these nebulae areunderestimated. However, the error on the ICF used to derive the carbon and oxygenabundance could be reduced with the aid of photo-ionization models or with the analysis ofrecombination lines from O2+ to O6+ (Barlow, private communication). This uncertaintydoes not apply to nitrogen and neon since high stages of ionization were measured, and there-fore the neon and nitrogen abundances are better determined than those of oxygen and carbon.

The error in the abundances in Table 5.3 is about 20 to 30%. These errors only includethe uncertainty in the intensities of the lines used to derive the abundances. Other errors, e.g.using Ionization Correction Factor (ICF) to derive abundances or the effect of uncertaintiesin the atomic parameters (especially the collisional strengths) are difficult to quantify. Theabundances shown in Table 5.3 have been derived using an ICF near unity. Often all important


stages of ionization are observed, in which case no error from the ICF is involved. Theabundances have been obtained using the most recent results available for the collisionalstrengths (mainly from the IRON project) so that these uncertainties are much reduced. Aquantitative idea of the errors on the abundance can also be inferred by looking at the sulfurand argon abundances in Fig. 5.2. Sulfur and argon are not supposed to vary in the course ofevolution, and as can be seen from the figure, they are within 30%. This strongly suggeststhat the abundance error derived from the intensity of the lines is the main contributor to thetotal error. Therefore 30% is a good estimate of the abundance error and has been assumedin this work for all nebulae except for the nitrogen abundance of NGC 6543 which has anerror 50%. This is because the main contribution to the nitrogen abundance comes from theN++ whose ionic abundance is derived either with the 57.3 µm or 1750 A lines. The formeris density dependent and the latter temperature dependent, increasing therefore the error (seechapter 4). The error in the helium abundance is around 5% except, again, for NGC 6543where it is 7-8%.

5.3.2 Comparison with Solar abundances

The PNe abundances (Table 5.3) are shown in Fig. 5.2 with respect to the solar. The typicalerror bar applies to all elements except helium for which the error is 6 times smaller. Thiscomparison is important because in principle one might expect that the progenitor stars ofthese PNe have evolved from a solar metallicity. Therefore, primary elements that do notchange in the course of evolution should lie close to the solar line, elements that are destroyedor produced should lie below or above.

An inspection of the figure leads to several conclusions. NGC 7662 shows low abun-dances for all elements. It is then suspected that the progenitor mass of this PNe was low andthat it did not experience much change in the course of evolution.

All other PNe show a He enhancement, which should be expected as He is brought to thesurface in the different dredge-up episodes. Four PNe show a decrease in carbon, especiallyNGC 6302 and He 2-111. The remaining PNe show solar or enhanced carbon. All PNe(except NGC 7662) show an increase of nitrogen. The oxygen abundance is close to solar forall PNe except three. The exceptions are NGC 6302, NGC 6537 and He 2-111 which show aclear decrease. It should be noticed that the solar abundance adopted in this work is that ofAllende Prieto et al. (2001). If the value of Grevesse & Sauval (1998) had been adopted allPNe would lie below the solar value.

Within the errors all neon abundances except that of NGC 7662 agree with solar. Of allelements neon is probably the best determined and it is likely that the error is somewhatsmaller than 30%. In this sense it is interesting to see how PNe with higher neon abundancesare clumped at around 0.15 and the three with lower values also have lower helium abundanceof the sample.

The remaining elements, sulfur and argon, are supposed to remain unchanged in thecourse of evolution and therefore should be close to solar. The argon abundance is com-patible with this but the sulfur abundance is lower than solar.

5.4. Nucleosynthesis in low- and intermediate-mass stars 79

5.4 Nucleosynthesis in low- and intermediate-mass stars

We will recall the main nucleosynthetic and convective mixing events that may possibly alterthe surface chemical composition of a low-/intermediate-mass star in the course of its evolu-tion. According to the classical scenario1 four processes are important (see e.g. Forestini &Charbonnel 1997 for a recent extended analysis), namely:

The first dredge-up. At the base of the RGB the outer convective envelope reaches regionsof partial hydrogen burning (CN cycle). As a consequence, the surface abundance of 4He isincreased (and that of H depleted), 14N and 13C are enhanced at the expense of 12C, while16O remains almost unchanged.

The second dredge-up. This occurs in stars initially more massive than 3-5 M� (depend-ing on composition) during the early AGB phase. The convective envelope penetrates intothe helium core (the H-burning shell is extinguished) so that the surface abundances of 4Heand 14N increase, while those of 12C, 13C and 16O decrease.

The third dredge-up. This takes place during the TP-AGB evolution in stars more massivethan ≈ 1.5M� for solar composition, starting at lower masses for lower metallicities (seeMarigo et al. 1999). It actually consists of several mixing episodes occurring at thermalpulses during which significant amounts of 4He and 12C, and smaller quantities of othernewly-synthesized products (e.g. 16O, 22Ne, 25Mg, s-process elements) are convected to thesurface.

Hot bottom burning. This occurs in the most massive and luminous AGB stars (with ini-tial masses M & 4− 4.5M�, depending on metallicity). The convective envelope penetratesdeeply into the hydrogen-burning shell, and the CN-cycle nucleosynthesis actually occursin the deepest envelope layers of the star. As a consequence, besides the synthesis of newhelium, 12C is first converted into 13C and then into 14N. In the case of high temperaturesand after a sufficiently long time, the ON cycle can also be activated, so that 16O is burnedinto 14N.

It should be remarked that the third dredge-up and hot-bottom burning are the processesthat are expected to produce the most significant changes in CNO and He surface abundances,being affected at the same time by the largest uncertainties in the theory of stellar evolution.This latter point motivates the adoption of free parameters (e.g. the dredge-up efficiency) todescribe these processes in synthetic TP-AGB models, that are discussed next.

5.5 Synthetic TP-AGB calculations

In order to interpret the abundance data reported in Sect. 5.3.1, synthetic evolutionary calcu-lations of the TP-AGB phase have been carried out with the aid of the model developed byMarigo et al. (1996, 1998, 1999), Marigo (1998, 2001, 2002), to whom we refer for all details.

1We do not consider here any additional extra-mixing process, such as the one invoked to explain the observedabundance anomalies in low-mass RGB stars (see e.g. Charbonnel 1995).

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Table 5.4–. Assumptions adopted in the TP-AGB synthetic calculations discussed in the paper.

3rd D-up efficiency Inter-shell composition Initial oxygen abundance

Models (ref.) Z Opacity1 λ2 Xcsh(12C) Xcsh(16O) Xcsh(4He) X0(O)3

A) Figs. 5.3, 5.9 0.019 κfix const. 0.50 0.220 0.020 0.760 O� HighB) Fig. 5.6 0.019 κvar const. 0.50 0.220 0.020 0.760 O� HighC) Fig. 5.6 0.019 κvar var. 0.457 0.220 0.020 0.760 O� HighD) Fig. 5.6, 5.11, 5.12 0.019 κvar var. 0.457 0.220 0.020 0.760 O� LowE) Fig. 5.6, 5.11, 5.12 0.019 κvar var. 0.30 0.220 0.020 0.760 O� LowF) Figs. 5.9, 5.11, 5.12 0.019 κvar var. 0.88, 0.96 0.050 0.005 0.945 O� LowG) Fig. 5.10 0.008 κfix const. 0.50 0.220 0.020 0.760 (Z/Z�)× (O� High)H) Fig. 5.10 0.008 κfix const. 0.90 0.220 0.020 0.760 (Z/Z�)× (O� High)I) Fig. 5.10 0.008 κvar const. 0.90 0.220 0.020 0.760 (Z/Z�)× (O� High)J) Figs. 5.10, 5.11, 5.12 0.008 κvar const. 0.90 0.030 0.001 0.969 (Z/Z�)× (O� High)K) Figs. 5.10, 5.11, 5.12 0.008 κvar const. 0.90 0.010 0.001 0.999 (Z/Z�)× (O� High)

1 “κfix” corresponds to solar-scaled molecular opacities by Alexander & Ferguson (1994);“κvar” denotes the variable molecular opacities as calculated according to Marigo (2002).

2 “const. value” means that the same constant value of λ is adopted at each dredge-up episode;“var. value” means that λ is made vary up to a maximum value, according to the analytic recipe by Karakas et al. (2002, their equation 7)

3 “O� High” refers the determination of the oxygen abundance for the Sun by Anders & Grevesse (1989);“O� Low” refers to the recent determination of the oxygen abundance for the Sun by Allende Prieto et al. (2001).

Other assumptions common to all TP-AGB models are:– log T dred

b = 6.4 following Marigo et al. (1999);– Mixing-length parameter α = Λ/Hp = 1.68 (where Hp denotes the pressure-scale height, and Λ is the mixing-length) following Girardi et al. (2000),

unless otherwise specified;–Nuclear reaction rates from Caughlan & Fowler (1988).

5.5. Synthetic TP-AGB calculations 81

We briefly recall that the initial conditions at the first thermal pulse are extracted fromfull stellar models with convective overshooting by Girardi et al. (2000). The consideredmass interval (0.7− 5.0M�) covers the whole class of low- and intermediate-mass stars thatdevelop an electron-degenerate C-O core at the end of the core He-burning phase. In thesemodels the initial chemical composition is taken from Anders & Grevesse (1989) for solarmetallicity (Z = 0.019), while for other metallicities solar-scaled abundances are assumed.

The Girardi et al. (2000) models predict the changes (if any) in the surface chemicalcomposition occurring prior to the TP-AGB phase by the first dredge-up during the firstsettling on the Red Giant Branch, and by the second dredge-up in stars of intermediate mass(say M > 3.5 − 4M�) during the Early AGB phase.

The subsequent TP-AGB evolution is calculated from the first thermal pulse up to thecomplete ejection of the envelope by stellar winds. Mass loss is included according to theVassiliadis & Wood’s (1993) formalism. The TP-AGB model predicts the changes in thesurface chemical composition caused by the third dredge-up and HBB. The third dredge-upis parametrized as a function of the efficiency, λ, and the minimum temperature at the baseof the convective envelope, T dred

b , required for dredge-up to occur (Marigo et al. 1999, seealso Sect. 5.5.1). The process of HBB – expected to take place in the most massive andluminous AGB stars (& 4.5M� depending on metallicity) – is followed in detail with theaid of a complete envelope model including the main nuclear reactions of the CNO cycle(Marigo et al. 1998; Marigo 1998).

Recently Marigo (2002) has introduced a major novelty in the TP-AGB model, thatis the replacement of fixed solar-scaled molecular opacities – commonly adopted inmost AGB evolution codes (kfix) – with variable molecular opacities (kvar) which areconsistently coupled with the actual elemental abundances of the outer stellar layers. Theimpact of this new prescription on the evolution of AGB stars is significant and consequently,as will be shown below, it importantly affects the predictions of the PN elemental abundances.

For the sake of clarity, in the following we will provide an outline of the main inputassumptions adopted in our TP-AGB calculations (Sect. 5.5.1 and Table 5.4).

5.5.1 Nucleosynthesis and mixing assumptions of the TP-AGB model

The treatment of the third dredge-up in the TP-AGB model is characterized by:

• A temperature criterion to establish whether a dredge-up episode does or does not oc-cur. It is based on the parameter T dred

b , that corresponds to the minimum temperature– at the base of the convective envelope at the stage of post-flash luminosity maximum– required for dredge-up to take place. In practice a procedure, based on envelope inte-grations, allows one to determine the onset of the third dredge-up, that is the minimumcore mass Mmin

c , and luminosity at the first mixing episode. More details can be foundin Marigo et al. (1999; see also Wood 1981, Boothroyd & Sackmann 1988, Karakas etal. 2002).

• The efficiency λ = ∆Mdred/∆Mc. It is defined as the fraction of the core massincrement, ∆Mc, over a quiescent inter-pulse period, that is dredged-up to the surfaceat the next thermal pulse (corresponding to a mass ∆Mdred).


• The composition of the convective inter-shell (in terms of the elemental abundancesXcsh,i) developed at thermal pulses, i.e. of the dredged-up material. We essen-tially specify the abundances of helium Xcsh(4He), carbon Xcsh(12C), and oxygenXcsh(12O) (see Table 5.4). We recall that detailed calculations of thermal pulsesindicate a typical inter-shell composition [Xcsh(4He) ∼ 0.76; Xcsh(12C) ∼ 0.22;Xcsh(16O) ∼ 0.02] (see e.g. Boothroyd & Sackmann 1988a; Forestini & Charbonnel1997). However, these results may drastically change with the inclusion of extendedovershooting from convective boundaries (i.e. Xcsh(12C) ∼ 0.50; Xcsh(16O) ∼ 0.25according to Herwig et al. 1997), or in the most massive TP-AGB models with deepdredge-up penetration (i.e. Vassiliadis & Wood 1993; Frost et al. 1998). This latterpossibility, relevant to our analysis, is discussed in Sect. 5.6.4.

In addition to 4He, 12C, and 16O, we account for the possible production of 22Ne,via the chain of reactions 14N(α, γ) 18F(β+, ν) 18O(α, γ) 22Ne (Iben & Renzini1983). Then a certain amount of 22Ne may be burned via the neutron source reaction22Ne(α, n)25Mg. The efficiency of this nuclear step strongly depends on the maximumtemperature achieved at the bottom of the inter-shell developed at thermal pulses,being marginal for T < 3 × 108 K (about 1 % of 22Ne is converted into 25Mg), whilebecoming more and more important at higher temperatures (Busso et al. 1999).

In our study, we parameterize the Ne and Mg production assuming that the abundancesin the convective intershell are given by (see also Marigo et al. 1996):

Xcsh(22Ne) = Xe(22Ne) + F ×

22

14× XHsh(14N) (5.1)

Xcsh(25Mg) = Xe(25Mg) + (1 − F ) ×

25

14× XHsh(14N)

where Xe refers to the envelope abundance before the dredge-up, and F representsthe degree of efficiency of the 22Ne production, that is clearly complementary to thatof 25Mg (1 − F ). In most of our calculations we assume F = 0.99, that meansallowing the chain of α-capture reactions to proceed from 14N to 22Ne, with essentiallyno further production of 25Mg. This point is discussed in Sect. 5.6.4.

In the above equations XHsh(14N) denotes the nitrogen abundance left by the H-burning shell in the underlying inter-shell region, just before the occurrence of thepulse. It is estimated with

XHsh(14N) = 14 ×[

Xe(12C)

12+

Xe(13C)

13+

Xe(14N)

14+

Xe(15N)

15+

Xe(16O)

16+

Xe(17O)

17+

Xe(18O)

18

]

,

i.e. we assume that all CNO nuclei are converted in 14N, which is a good approximationwhen the CNO-cycle operates under equilibrium conditions. In this way we accountfor the possible primary component of 14N in the inter-shell, which is produced every

5.6. Comparison between models and observations 83

time some freshly dredged-up 12C in the envelope is engulfed by the H-burning shellduring the quiescent inter-pulse evolution.

As a consequence, the resulting Xcsh(22Ne), synthesized via the chain of Eq. (5.1),contains a primary component, which can also be injected into the surface chemicalcomposition through the dredge-up. We note that 22Ne is expected to be purely sec-ondary in low-mass stars that do not experience the third dredge-up.

The reader can find more details about model prescriptions in Table 5.4.

5.6 Comparison between models and observations

We will now perform an analysis of the observed PN elemental abundances with the aid ofthe TP-AGB models just described. The basic idea is to constrain the model parameters so asto reproduce the observed data, and hence derive indications on the evolution and nucleosyn-thesis of AGB stellar progenitors. The chemical elements under consideration are He, C, N,O and Ne.

5.6.1 The starting point: TP-AGB models with solar-scaled molecular opacities

First “old” predictions of PN abundances (Marigo 2001) are considered; see Fig. 5.3. In thosemodels with an initially solar composition the dredge-up parameters (λ and T dred

b ) werecalibrated to reproduce the observed carbon star luminosity functions in both MagellanicClouds (Marigo et al. 1999). Moreover, envelope integrations were carried out using fixedsolar-scaled molecular opacities (κfix; see Sect. 5.5).

By inspecting Fig. 5.3 we note that, though a general agreement is found between mea-sured and predicted abundances with respect to nitrogen and neon abundances, three maindiscrepancy points occur:

1. A sizeable overproduction of carbon by models, up to a factor of 3-5;

2. The lack of extremely He-rich models, with 0.15 < He/H ≤ 0.20;

3. A general overabundance of oxygen in all models, amounting up to a factor of 3.

While the first two aspects are probably related to the nucleosynthetic assumptions inthe TP-AGB models, the third one could also reflect our choice of oxygen abundance in thesolar mixture (Anders & Grevesse 1989), which has recently been subject of major revision(Allende Prieto et al. 2001). The aim of the following analysis is to single out the main causesof the disagreement and possibly to remove it by proper changes in the model assumptions.

5.6.2 Sub-grouping of the ISO sample and comparison with other PNe data

Before starting the interpretative analysis, it is worth noticing that the PNe data (see Fig. 5.3)seem to segregate in two different groups in the observational abundance plots – one atlower (He/H ≤ 0.14) and the other at higher helium content (He/H > 0.14) –, and theirchemical patterns for carbon and nitrogen already suggest likely different mass ranges forthe progenitors (i.e. low- and intermediate-mass stars respectively).


Figure 5.3–. Comparison between measured PN abundances (squares with errors bars) and modelpredictions (diamonds). Two estimates for the oxygen abundance for the Sun are also indicated, O�

High and O� Low (see Table 5.4 and text). In each panel the sequence of diamonds denotes the expectedPN abundance as a function of the stellar progenitor’s mass, increasing from 0.9 to 5.0 M� (a few valuesare labeled along C/H curve), and for initial solar metallicity Z = 0.019. The initial O abundance wasset equal to O� High. The model assumptions adopted for the TP-AGB evolution, corresponding tocase A) of Table 5.4, include solar-scaled molecular opacities (κfix), and third dredge-up efficiencyλ = 0.5.


Figure 5.4–. Comparison of PN abundances from our ISO sample (filled squares) and other samples inthe literature, namely: Henry et al. (2000; open triangles) and Kingsburgh & Barlow (1994; diamonds)for PNe in the Milky Way, and Dopita et al. (1997; filled triangles) for PNe in the LMC. The ISOsample has been plotted using smaller and larger squares for PNe with helium abundances lower andhigher than 0.145 respectively.

In particular, there are three PNe, He 2-111, NGC 6302 and NGC 6537 that clearly showthe highest helium abundance (He/H >0.14) together with the lowest carbon and oxygenabundances. To this respect we recall that it was recognized a long time ago (Becker &Iben 1980) that the observed N/O-He/H correlation and the C/O-N/O anti-correlation –characterising the He-rich PNe – present a problem for models of nucleosynthesis on theAGB. This will be discuss in Sect. 5.6.4.

Comparison with literature data on PN elemental abundances provides further support fortwo separate groups of PNe according to their helium content, “normal” or high. Figure 5.4compares our observed abundances with data from Henry et al. (2000) and Kingsburgh &Barlow (1994) for PNe in the Milky Way, and from Dopita et al. (1997) for PNe in the LMC.Only PNe with measured C abundances and not already present in the ISO sample have beenincluded. The reader should bear in mind that excluding helium, the errors on the remainingabundances of these two samples are large and uncertain.


The “normal” helium group in the ISO sample (with He/H < 0.145; smaller filled squares)is within the range of abundances given by Henry et al. (2000) and Kingsburgh & Barlow(1994). However, both studies lack PNe with high He abundances. Actually, PN PB 6 (fromHenry et al. 2000 sample) has a helium abundance of 0.2 but that value is highly uncertain,and 0.146 is the highest helium abundance among those PNe that we have excluded from theKingsburgh & Barlow (1994) sample (those with no measured carbon).

Conversely, the three ISO PNe with high helium abundances (with He/H > 0.145; largerfilled squares) agree well with the LMC PNe from Dopita et al. (1997), not only in the Heabundance but also in the N/O and C/N ratios. Besides supporting the division of the ISOsample into two subclasses, this also suggests that an initial sub-solar metallicity may be akey factor in the subsequent nucleosynthesis.

For all these reasons, it seems advantageous to separate those PNe which exhibit highhelium content from the others having “normal” helium abundances, and to discuss the twogroups separately.

5.6.3 PNe with “normal” He abundances

Let us examine the PN data with He/H. 0.14 (Fig. 5.3). For the sake of clarity we summarisethe main features pointed out in Sect. 5.3.1.

• Most of the data present a clear enhancement in He, C, N compared to the abundancesof these elements for the Sun. In particular, some of them should descend from carbonstars given their C/O ratio larger than one.

• Oxygen abundances are underabundant when compared to the Solar determination byAnders & Grevesse (1989). On the other hand they are consistent with a constant, orslightly increasing trend with He/H, if compared to the recent oxygen estimation forthe Sun by Allende Prieto et al. (2001).

• Neon seems to exhibit a constant, or perhaps moderately increasing trend with He/H.

We first consider the elemental changes expected after the first and second dredge-upepisodes. The predicted envelope abundances are displayed in Figure 5.5 for two values ofthe initial metallicity, i.e. Z = 0.019 and Z = 0.008. Compared to their original valuesoxygen and neon are essentially unaffected, carbon is somewhat reduced, while nitrogenand helium may be significantly increased particularly after the second dredge-up in stars ofintermediate mass (M > 4M�).

The comparison with the PN data indicates the necessity to invoke further chemicalchanges in addition to those caused by the first and second dredge-up, especially if oneconsiders the observed enhancement in carbon. The most natural explanation resides in thethird dredge-up process occurring during the TP-AGB phase. To this respect, as alreadymentioned in Sect. 5.6.1, the “old” models with fixed solar-scaled molecular opacities predicttoo large carbon enrichment (Fig. 5.3). This point and its possible solution are discussedbelow.


Figure 5.5–. Observed PN abundances (squares with error bars) compared to expected surface abun-dances (taken from Girardi et al. 2000) just before the onset of the TP-AGB phase, as a function ofthe initial stellar mass, and for two values of the original metallicity, i.e. Z = 0.019 (upper curves)and Z = 0.008 (lower curves). The initial mass ranges from 0.6 to 5.0 M� at increasing He/H alongthe curves. Predicted abundances are those expected after the first dredge-up (solid line) for stars with0.6 ≤ M/M� ≤ 4.0; and after the second dredge-up (dashed line) for stars with 4.0 < M/M� ≤ 5.0.


Figure 5.6–. Carbon abundances and C/O ratios in PNe with low helium abundances (He/H≤ 0.13).Open symbols denote predictions of synthetic TP-AGB calculations for various choices of model pa-rameters – specified in the legenda – corresponding to a stellar progenitor with (Mi = 2.0M�, Zi =0.019). See text and cases B-C-D-E of Table 5.4 for more details.

Reproducing the extent of carbon enrichment

To tackle the problem of carbon we consider a stellar model with 2M� initial mass, a typicalmass of carbon stars in the Galactic disk (Groenewegen et al. 1995). Figure 5.6 shows a fewmodels of the predicted carbon abundance and corresponding PN values.

As starting model we consider the one with the κfix assumption. It is clearly located wellabove the observed points (diamond in left panel of Fig. 5.6).

A first significant improvement is obtained acting on the opacity, that is adopting vari-able molecular opacities during the TP-AGB calculations. We replace κfix with κvar, whilekeeping the other model parameters fixed. In this model (starred symbol) the predicted C/His lowered because of a shorter C-star phase, hence a decrease in the number of dredge-upepisodes (see Marigo 2002, 2003).

Additional cases are explored. The usual assumption of constant dredge-up efficiency λis replaced with the recent recipe by Karakas et al. (2002), who provide analytic relations– fitting the results of full AGB calculations – that express the evolution of λ as a functionof metallicity Z, stellar mass M , and progressive pulse number. For a given M and Z, λ isfound to increase from initially zero up to nearly constant maximum value, λmax. This latteralso varies depending on mass loss. Adopting λmax = 0.457 as suggested by Karakas et al.(2002) for the (M = 2M�, Z = 0.02) combination, we end up with a somewhat lower C/H(triangle), compared to the case with (κvar, λ = 0.5). This reflects the smaller amount ofcarbon globally dredged-up with the λvar assumption.


A further test is made with respect to the assumed initial oxygen abundance. We calculatethe TP-AGB evolution of the 2M� model replacing the surface oxygen abundance at thefirst thermal pulse – as predicted by Girardi et al. (2000) evolutionary calculations, basedon Anders & Grevesse (1989) solar mixture (the O� High in Table 5.4) – by the recentlyrevised determination by Allende Prieto et al. (2001; the O� Low in Table 5.4).

With the new lower oxygen abundance the solar C/O ratio increases from 0.48 to 0.78.This increment in the initial C/O ratio has important effects on the later TP-AGB evolutionand PN abundances: fewer dredge-up episodes are necessary to produce a carbon star andhence, on average, a lower C abundance is expected in the PN ejecta. This can be seen inFig. 5.6, by comparing the models labeled by triangle and circle symbols. We also noticethat the trend in the predicted values of C/H (left panel) or C/O (right panel) is reversed.The O� Low prescription leads to a reduced absolute carbon enrichment compared to theO� High case, while the final C/O ratio is larger in the former case. It should be remarkedthat using the recent carbon abundance by Allende Prieto et al. (2002) together with the newlower oxygen abundance the C/O ratio is 0.50, nearly equally to the ratio of Grevesse &Noels (1993), negating the above comment.

At this point the results already appear better compared to the starting model, but inorder to carry the expected C/H point within the observational error bars, we change anotherfundamental model parameter, i.e. the dredge-up efficiency λ. A good fit of the PNe data isobtained by lowering λmax from 0.457 to 0.3, that simply means diminishing the amount ofdredged-up carbon.

In summary, from these calculations we derive the following indications. Both the C/Hand the C/O ratios of the carbon-rich Galactic PNe – evolved from stars with typical massesof ∼ 2.0M� – can be reproduced by assuming i) variable molecular opacities κvar, ii)an initial oxygen abundance as recently revised by Allende Prieto et al. (2001), and iii)a dredge-up efficiency λ ≈ 0.3 − 0.4. These indications – in particular points i) and iii)– agree with the results recently obtained by Marigo (2002, 2003) in her analysis of theproperties of Galactic carbon stars in the disk. Variable molecular opacities and λ . 0.5 arerequired to reproduce a number of observables of carbon stars, like their C/O ratios, effectivetemperatures, mass-loss rates, and near-infrared colours.

Then, from the representative case of the 2.0M� model, we consider a wider mass range,i.e. 1.1 − 5.0M�, with initial metallicity Z = 0.019. Results of the C/H and C/O ratios asa function of He/H, expected in the corresponding PNe, are displayed in Figs. 5.7 and 5.8and are also summarized in the top-left panels of Figs. 5.11 and 5.12 (triangles connectedby solid line). They show a satisfactory agreement with the observed data for He/H< 0.14,suggesting a mass interval for the stellar progenitors from about 1.0 to 4.0 M�.

Synthetic TP-AGB calculations are carried out by adopting the κvar and O� Lowprescriptions, and assuming λ ≈ 0.3 − 0.5 for lower stellar masses (M . 3.0M�), whileincreasing it up to λ ≈ 0.98 for the largest masses. This means that the third dredge-upshould become deeper in more massive stars, as indicated by full TP-AGB calculations


(e.g. Vassiliadis & Wood 1993; Karakas et al. 2002). It is worth noticing that models withM ≤ 1.5M� are predicted not to experience the third dredge-up, i.e. they do not fulfil theadopted temperature criterion (based on the parameter T dred

b ; refer to Sect. 5.5.1).

Moreover, we assume that in the most massive stars (with M = 4.0 − 5.0M�) thecomposition of the inter-shell may be different from the standard one, i.e. less primary carbonis supposed to be synthesised during thermal pulses. This point will be discussed in moredetail in Sect. 5.6.4.

Other elemental abundances

As for the He, N, O, Ne elemental abundances, we can outline the following (see sequencesof triangles in Figs. 5.11, 5.12):

• The helium abundance up to He/H∼ 0.14 is well reproduced by accounting for the sur-face enrichment due to the first, and possibly second and third dredge-up. Apparently,for this group of PNe, there is no need to invoke a significant production of helium byHBB. We also notice that the minimum value predicted by stellar models with initialsolar composition is He/H∼ 0.096, so that any observed value lower than that (e.g.NGC 7662) may correspond to a stellar progenitor with lower initial metallicity andhelium content.

• The nitrogen data are consistent, on average, with the expected enrichment producedby the first and second dredge-up events.

• As already discussed, the PN oxygen estimates are compatible with the recent revisionfor the abundance in the Sun by Allende Prieto et al. (2001; (O/H�) = 4.9 × 10−4).The PN data indicate that during the evolution of the stellar progenitors, their surfaceabundance of oxygen is essentially unchanged, or it might be somewhat enhanced.Anyhow, the revised lower determination for the Sun removes the problem of ex-plaining the systematic oxygen under-abundance compared to solar that all data wouldpresent if adopting higher values for the Sun as indicated by past analyses (e.g. Anders& Grevesse 1989; (O/H)� = 7.4 × 10−4).

• The neon data do not allow to put stringent constraints on the nucleosynthesis of thiselement in TP-AGB stars with initial solar metallicity. In fact, within the uncertaintiesthe observed Ne/H abundances are compatible with a preservation of the original value,but they can also point to a moderate increase.

Predictions shown in Fig. 5.11 are obtained under the assumption that the synthesis of22Ne – via α-captures in the He-burning shell starting from 14N during thermal pulses– takes place with almost maximum possible efficiency (F = 0.99, see Sect. 5.5.1).As we see, the final expected enrichment in PNe remains modest, due to the relativelysmall number of thermal pulses and moderate dredge-up efficiency (λ ∼ 0.3 − 0.5)characterising TP-AGB models with initial masses M ∼ 1.5−3.0 M�, and metallicityZ = 0.019.

The opposite situation, that is the complete conversion of 22Ne into 25Mg with F ∼0, would not lead to any enrichment in neon so that the sequence of predicted Ne/H


Figure 5.7–. Summary of the results that best fit the observed PN abundances for He/H≤ 0.14.Specifically, triangles represent predictions derived from TP-AGB models with Z = 0.019 and withinitial stellar masses from 1.1 to 5.0 M�, and adopting the following prescriptions summarised in Ta-ble 5.4: case E) for 1.1 ≤ M/M� ≤ 2.5; case D) for M = 3.0 M�; case F) for 3.5 ≤ M/M� ≤ 5.0.In practice, we assume the efficiency of the third dredge-up changes during the evolution (accordingto Karakas et al. 2002), and increases with the stellar mass. Note that also the composition of theconvective inter-shell varies as a function of the stellar mass, i.e. less primary carbon is supposed to besynthesised during thermal pulses by models with the largest masses. See text for more details.


Figure 5.8–. The same as in Fig. 5.7, but expressing the abundance data with different combinationsof elemental ratios.

would be flatter2 than the present one (connected triangles in Fig. 5.11). But this casecould not be rejected either since corresponding predictions are still confined withinthe observed domain.

5.6.4 PNe with extremely high He abundance

Below we discuss the PNe exhibiting the largest enrichment in helium, i.e. with 0.14 .

He/H. 0.20 (see e.g. Fig. 5.3). These objects share other chemical properties, namely:

• Marked carbon deficiency compared to the solar value;

• Sizeable enhancement of nitrogen, but not exceeding the upper values observed in thePNe with lower He/H;

• Significant depletion of oxygen, which makes these PNe appear as a distinct groupwith respect to the PNe with lower He/H abundances;

• Possible, but still not compelling, hint of over-abundance of neon compared to the solarvalue.

By looking at Fig. 5.5, we conclude that model predictions after the first and seconddredge-up processes cannot account for the extremely high He/H values of these PNe. Then,

2In any case Ne/H should keep a slightly increasing trend, not becoming exactly horizontal since, even if Ne=const., the hydrogen content H decreases as a consequence of dredge-up events.


we are led to consider additional He contributions from the third dredge-up and HBB duringthe TP-AGB phase.

Qualitatively, the enrichment in helium and nitrogen and the simultaneous deficiency incarbon would naturally point to HBB as a possible responsible process, via the CNO-cyclereactions. Therefore, as a working hypothesis, let us assume that the stellar progenitors ofthese extremely He-rich PNe are intermediate-mass stars (M & 4.5M�), experiencing HBBduring their AGB evolution. We will now investigate under which conditions all elementalfeatures can be reproduced.

To allow an easier understanding of the following analysis, Figs. 5.9 and 5.10 show thepredicted time evolution of He, C, N, O, and Ne elemental abundances in the envelope dur-ing the TP-AGB phase of models experiencing HBB. Different assumptions are explored.The observed PN abundances should be compared with the last starred point along the the-oretical curves, which marks the last event of mass ejection, and it may be then consideredrepresentative of the expected PN abundances.

Constraints from oxygen and sulfur abundances

At this point additional information comes from the marked oxygen under-abundancecompared to solar (for both High and Low values), common to the extremely He-rich PNe.

We recall that the oxygen abundance in the envelope remains essentially unchanged afterthe first and second dredge-up events. The third dredge-up may potentially increase oxygen,depending on the chemical composition of the convective inter-shell that forms at thermalpulses. In any case, no oxygen depletion is expected by any of these processes. A destructionof oxygen could be caused by a very efficient HBB, that is if the ON cycle is activated andoxygen starts being transformed into nitrogen.

We have explored this possibility on a 5M� TP-AGB model with original solar metal-licity. To analyse the effects of a larger HBB efficiency, the mixing-length parameter αML

has been increased, and set equal to 1.68, 2.00, and 2.50. In fact, larger values of αML

correspond to higher temperatures at the base of the convective envelope. In none of thethree cases have we found any hint of oxygen destruction, as indicated by the flat behaviourof the abundance curves in the bottom-left panel of Fig. 5.9 (solid and long-dashed lines, forα = 1.68 and 2.50, respectively).

At this point we decided to stop further increasing α – which would have likely ledto oxygen destruction at some point – since we run into a major discrepancy. In fact,increasing the efficiency of HBB causes a systematic over-enrichment in nitrogen, as shownby the model with αML = 2.50 (short-dashed line). We also note that a significant nitrogenproduction is accompanied by a mirror-like destruction of carbon (upper-left panel ofFig. 5.9). This is not the case of the model with αML = 1.68 (solid line), in which HBB isalmost inoperative.

From these results we can expect that, even if a destruction of oxygen is obtained forlarger values of αML, the problem of nitrogen over-production would become even more


Figure 5.9–. Time evolution of surface elemental abundances during the TP-AGB phase of a 5.0M�

model with initial solar chemical composition, experiencing both the third dredge-up and HBB. Ob-served PN data should be compared with the starred symbol at the end of each curve (marking the endof the TP-AGB phase). Most parameter prescriptions are specified Table 5.4. In practice we considerthe following cases: i) efficient HBB with α = 2.50 (short-dashed line; refer to case A) of Table 5.4for other model parameters); ii) weak HBB with α = 1.68 (solid line; refer to case A) of Table 5.4);and iii) weak HBB and efficient dredge-up, starting from a lower oxygen abundance (long-dashed line;refer to case F) of Table 5.4).


severe. All these considerations suggest that the most He-rich PNe in the sample shouldnot descend from stars with original solar metallicity, but rather from more metal-poorprogenitors. In other words, the observed sub-solar oxygen abundances likely might reflectthe initial stellar metallicity.

To test the hypothesis of an original lower oxygen content we perform explorativeTP-AGB evolutionary calculations of intermediate-mass stars with initial LMC composition,characterised by roughly half-solar metallicity. The predicted envelope abundances afterthe first and second dredge-up for stellar models with [Z = 0.008, Y = 0.25] are shown inFig. 5.5. As we see the oxygen curve (bottom-left panel) is now lower than the correspondingone for solar composition, and it appears to be much more consistent, but not fully, with thelocation of the He-rich PNe. In the next subsections we will test whether these models areactually able to fulfil, besides the oxygen data, all other chemical constraints related to He,C, N, and Ne abundances. Finally, we note that even better results for O may be obtained byadopting an initial oxygen abundance for the LMC composition, scaled from the new solardetermination by Allende Prieto et al. (2001).

At this point it is important to stress the following. The suggestion that these threePNe have evolved from such a massive (∼4-5 M�) low metallicity progenitor is striking.Their strong bi-polarity, high nebular masses and low galactic latitude do not suggest a lowmetallicity progenitor. In Sect. 5.3.1, we saw that the nitrogen and neon abundances aremore accurately determined. These are similar to the normal PNe which are compatible witha solar initial metallicity. However, the high helium abundance cannot be reproduced frommodels starting with solar metallicity (see Fig. 5.7). To solve this particular problem, a moreefficient HBB is required, but this would increase the nitrogen abundance above the observedvalue. It may be that these models are missing an essential part of the physics. Furtherinvestigation of these models on this issue is certainly required. In particular, the inclusion ofthe recent (lower) carbon solar abundance by Allende Prieto et al. (2002) should also help inachieving the low observed carbon abundance. Since we want to simultaneously reproduceall the observed abundances (using the current models available) we shall continue with theassumption of a sub-solar (LMC) composition for these nebulae.

It is worth adding now some considerations about the possibility that the most He-richPNe in the sample evolved from stars with sub-solar metallicity.

On the one side, our proposed scenario may run into trouble if we suppose that the historyof chemical enrichment of our Galactic disk simply follows an age-metallicity relation, inwhich younger ages correspond to larger metallicities. In fact in this case, we would expectthat stars with initial masses as large as ∼ 5M� should form from gas with comparable, oreven higher, degree of metal enrichment than the Sun. However, more detailed considerationsshow that the assumption of a unique age-metallicity relation provides an over-simplifieddescription of the actual chemical evolution in the Galactic disk.

For instance, the Orion nebula has a lower metallicity than solar even though it isyounger. Also, in the solar neighborhood differences do exist. Edvardsson et al. (1993)studied a sample of nearly 200 F and G dwarfs in the Galactic disk and found a considerable[Fe/H] scatter even for stars with similar age and belonging to a nearby field of the disk.


They concluded from this that the chemical enrichment in the Galaxy is inhomogeneous.There is therefore a fraction of disk stars in the sky with different composition from solar.The three PNe with high He abundance belong to the disk and are indeed in the same partof the sky (within ±10◦ of the Galactic center). We may reasonably state that these objectsbelong to lowest tail of the metallicity distribution in the Galactic disk. These argumentssupport the use of a metallicity different from solar but do not point to LMC metallicity.Another weak point is that the metallicity generally increases towards the center of theGalaxy, while these PNe should have a lower metallicity.

An additional hint for a different initial composition from solar is given by sulfur. AllPNe in the sample display a clear under-abundance of sulfur with respect to solar (seeFig. 5.2), whereas this element is expected not to change in the course of stellar evolution.Its abundance in our PN sample is even lower than in Orion (see Table 5.3), which is ayoung stellar object. This implies that either the nucleosynthesis history of sulfur is not yetunderstood and it can actually be destroyed in the course of the evolution, or that the initialcomposition, at least of this element, can deviate from solar. Alternatively, the determinationof the solar abundance may be wrong. This possibility seems the most plausible. Thesulfur abundance is within the range of values given by Martın-Hernandez et al. (2002)for a sample of galactic H II regions. If the initial abundance of sulfur is not solar, thismay also be the case for the other elements. Maybe the He-rich PNe are consistent withsub-solar metallicities but, since all observed PNe are under-abundant in sulfur, we are left toexplain why for some PNe we need solar metallicity whereas for others a lower metallicityis invoked, this latter feature only applying to the most He-rich objects. This might be theresult of some, still unidentified, selection effect.

The PNe with high helium abundance also show the lowest (C+N+O)/H abundance (seeFig. 5.2). This, again, suggests a lower initial metallicity. Nevertheless the neon, sulfur andargon abundances are similar to the rest of planetaries which would in principle be againstthis suggestion. The similarity in neon of these three PNe with the rest can be explainedinvoking the production of neon in the course of evolution. The LMC sulfur abundance iscompatible with all the PNe in the sample. As discussed above it might be that the sulfursolar abundance is wrong since this is a primary element and the observed abundances arequite accurate. The argon is more tricky. All PNe show similar argon abundances whichare actually close to solar. The LMC argon abundance is much lower than that of the highhelium PNe. The discrepancy between the sub-solar sulfur and the solar argon abundance isnot readily explained.

These aspects still need to be clarified, but we would remark that a possible answer maycome in the context of a dedicated study of the chemical evolution of our Galaxy, which isbeyond the scope of the present work.

Constraints from carbon and nitrogen abundances

Perusal of the C/H and N/H curves in Fig. 5.5 (predicted after the first and second dredge-up)for the LMC composition, shows that they share the trends with the stellar mass as thesolar-metallicity curves, but the carbon and nitrogen abundances are now systematicallylower, as for oxygen. In particular carbon abundances, prior to the TP-AGB evolution, – at


Figure 5.10–. The same as in Fig. 5.9, but for initial LMC chemical composition. Illustrated casesmainly differ in the adopted parameters describing the third dredge-up, i.e. (see also Table 5.4): i) andii) moderate third dredge-up (λ = 0.5) and standard chemical composition of the inter-shell (case G)for 4.5 and 5.0 M� models (dotted and dot-short-dashed lines, respectively), iii) deep third dredge-up(λ = 0.9) and standard chemical composition of the inter-shell (case H) for 5.0 M� model (dot-long-dashed line); iv) the same as the previous case but for the κvar prescription (case I; short-long-dashedline); v), vi), and vii) deep third dredge-up (λ = 0.9) and inter-shell chemical composition with low-carbon abundance for 5.0 M� model (solid line and case J; short-dashed line and case K) and 4.5 M�

model (long-dashed line and case K).


any stellar mass – are now compatible with the low values measured in the He-rich PNe. Asfor nitrogen, some enrichment seems instead required (up to a factor of 2 at the largest stellarmasses) to obtain agreement with the observations.

Given these premises, a number of TP-AGB models with Z = 0.008 and masses of 4.0−5.0M� have been calculated for different choices of parameters, in view to simultaneouslymatching the observed carbon, nitrogen and helium abundances. We just summarise the mainemerging points.

Efficiency of the third dredge-up. High He abundances strongly depend on the efficiencyof the third dredge-up. Figure 5.10 shows that relatively low values of λ lead to inadequatehelium enrichment, because both a limited amount of helium is dredged-up at each thermalpulse, and the duration of the TP-AGB phase becomes shorter, implying fewer dredge-upevents. This is true for the TP-AGB models with M = 4.5, 5.0M�, and λ = 0.5 (dotted anddot-short-dashed curves), which do not go beyond He/H= 0.13.

On the other hand, TP-AGB models of the same initial masses but with λ ∼ 0.9 becomehighly enriched in helium, yielding a very close agreement with the observed data for He/H(solid, short-dashed, and long-dashed curves). The largest He/H values measured in PNeare reproduced under the assumption that massive TP-AGB stars experience, besides HBB, alarge number (of the order of 100) of very efficient third dredge-up episodes.

This indication is supported by recent results of full TP-AGB calculations for stellarmasses & 5M� (Vassiliadis & Wood 1993; Frost et al. 1998; Karakas et al. 2002).

The problem of nitrogen over-production. Invoking a large dredge-up efficiency doesnot guarantee, however, that all other elemental features are reproduced. In fact, assuminga very efficient dredge-up λ ∼ 0.9, and the standard intershell chemical composition (i.e.Xcsh(12C) = 0.22, Xcsh(16O) = 0.02, Xcsh(4He) = 0.76; see Sect. 5.5.1), we find asizeable over-production of nitrogen by HBB. This is illustrated in Fig. 5.10 by the N/H curvecorresponding to the 5M� model (with κfix prescription; dot-long-dashed line). Calculationswere stopped before the termination of the TP-AGB evolution (i.e. before the ejection of theentire envelope), since the He/H in the envelope already exceeded 0.2 and the over-productionof nitrogen was very large.

In relation to this latter point, going back to the past literature, the same problem wasalready pointed out by Marigo et al. (1998; see their section 5.4) and earlier by Becker & Iben(1980; see their section VII), in their careful analysis on the expected abundance variationsduring the TP-AGB phase of intermediate-mass stars and the observed PNe abundances (seetheir section VII). These authors demonstrated that the efficiency of HBB, required to achievethe small C/O values exhibited by PNe with large He/H, is such as to yield N/O ratios thatexceed by over an order of magnitude the PN values. This indication is quite robust andalmost model-independent, since it merely reflects the interplay between nuclear reactions ofthe CN-cycle. The efficiency of the third dredge-up directly affects the HBB nucleosynthesis:if the CN-cycle operates at equilibrium (a condition often met by stars with HBB) the morecarbon that is dredged-up, the more nitrogen is eventually synthesised.

After discussing various aspects of the issue, Becker & Iben (1980) concluded that thepositive correlation between N/O and He/H observed in helium-rich PNe could be reproduced“by supposing that 12C is burned at a modest rate in the convective envelope” of the most


massive TP-AGB stars. In other words, they invoked a weak efficiency of HBB. However,these authors also clearly stated that in this way one would at the same time cope with thediscrepancy of predicting too large atomic C/O ratios, contrary to observations. The onlypossible explanation, plausible at that time, to reconcile all points was the hypothesis of asignificant dust-depletion of carbon, with consequent apparent decrease of the measured C/Oratio (involving the atomic carbon). In this study we explore other possibilities, as reportedbelow.

The effect of variable molecular opacities. First we consider the effect of variable molec-ular opacities. Replacing the κfix with κvar prescription in the 5M� model (while keepingλ = 0.9, and the standard chemical composition), the evolution of He, C, N surface abun-dances change dramatically. In practice, we pass from the problem of a huge nitrogen over-production for the κfix case (dot-long-dashed N/H curve) to those of almost zero nitrogensynthesis and carbon over-enrichment for the κvar model (short-long-dashed line).

The latter result is due to the weakening, or even prevention, of HBB in intermediate-mass stars that undergo efficient carbon enrichment by the third dredge-up during the earlystages of their TP-AGB evolution. As discussed by Marigo (2003), the increase in molecularopacities, as soon as C/O becomes larger than one, causes cooling at the base of the convectiveenvelope, which may extinguish the CNO-cycle reactions associated with HBB.

Both models with different opacities do not reproduce the observed PN data for C and N,though both seem to imply the same direction: too much carbon is assumed to be injected bythe third dredge-up into the convective envelope. This causes the over-production of nitrogenin the κfix model, while it yields a net over-enrichment of carbon in the κvar model.

These considerations introduce us to another possibility to solve this problem, related tothe chemical composition of the convective inter-shell.

Inter-shell chemical composition. We propose here a solution, different from that sug-gested by Becker & Iben (1980), to account simultaneously for the observed N/O and He/Hcorrelation and C/O and He/H anti-correlation. It is based on the assumed elemental abun-dances – essentially 4He, 12C, and 16O – in the convective inter-shell developed at thermalpulses, part of which is then dredged-up to the surface.

We find that all discrepancies – relative to the N and/or C over-production – are re-moved by relaxing the usual prescription of the standard inter-shell chemical composition(Boothroyd & Sackmann 1998, see also Sect. 5.5.1, and Table 5.4), and assuming insteadthat the dredged-up material in intermediate-mass TP-AGB stars consists mainly of helium,with very little carbon and practically no oxygen. Results are shown in Fig. 5.10 (solid, short-and long-dashed curves). Thanks to the small amount of dredged-up carbon, we would favourthe enrichment in helium and avoid the nitrogen over-production.

These indications have been initially derived from empirical evidence, and it is encour-aging to receive also some theoretical support from calculations of the TP-AGB evolution ofintermediate-mass stars. To our knowledge, it was first mentioned – that the typical chemi-cal inter-shell composition may be quite different from the standard one in the most massiveTP-AGB stars – in the work of Vassiliadis & Wood (1993). The authors point out that thethermal pulses in TP-AGB stars as massive as 5M� are characterised by extremely deepdredge-up (λ ≈ 0.8), and weak efficiency of the triple-α reaction in the convective inter-shelldue to both the rapid quenching of the instability. These authors state that in their calculations


the dredged-up material mainly consists of helium and nitrogen produced by the CNO cycle.Consequently, this result should imply a lower synthesis of primary carbon in the convectiveinter-shell, hence a lower carbon abundance in the dredged-up material compared to the stan-dard values (Xcsh(12C) < 0.2 − 0.3). This indication agrees with our suggestion to explainthe measured CNO abundances in PNe with very high helium content.

A few years later, Frost et al. (1998) partly confirmed the results by Vassiliadis & Wood(1993), and pushed the analysis further reporting the discovery of a new kind of thermalpulses, designated as “degenerate thermal pulses” (the reader should refer to that work for alldetails). In few words a massive TP-AGB star would experience a sort of cyclic trend: Firsta relatively large number of weak thermal pulses (say 30 − 40) with very deep dredge-uptakes place leaving a long tail of unburned helium, that is then burned at once by a strong“degenerate pulse” (the carbon abundance in the inter-shell reaches 12C ≈ 0.6), after whichanother sequence of weak pulses starts again, and so on. Similar trends have been reportedby Siess et al. (2002) in their study of the TP-AGB evolution in population III stars.

It should be remarked that while there is a close agreement in the results by Frost etal. (1998) and Vassiliadis & Wood (1993) with respect to the high efficiency of the thirddredge-up (λ ≈ 1) in these massive AGB stars, some substantial differences could be presentinstead in the predicted chemical composition of the dredged-up material. In fact, thepossibility of a carbon abundance lower than the standard value (Xcsh(12C) < 0.2 − 0.3),which is deduced from the Vassiliadis & Wood’s paper, is actually not confirmed by the workof Frost et al. (1998; also Lattanzio’s private communication). These possible differencescould be ascribed to different physical and numerical details of the stellar evolution codes,that can significantly affect the results (see Frost et al. 1998; Frost & Lattanzio 1996; andLattanzio’s private communication).

We believe that this point is crucial and it deserves a clarification with the aid of full cal-culations of the thermal pulses experienced by the most massive AGB models. Anyway, asour study represents a sort of empirical calibration of the AGB nucleosynthesis, we followVassiliadis & Wood’s indications and assume the possibility that during their TP-AGB evolu-tion the most massive intermediate-mass stars suffer many deep dredge-up events that bringa large amount of helium, but little carbon up to the surface. In fact, as mentioned above,this seems just what we need to reproduce the observed abundances of the most He-rich PNe,thus solving a long-standing problem already stated by Becker & Iben (1980).

The quantitative confirmation comes from the results of our TP-AGB calculations pre-sented in Fig. 5.10, referring to models with i) stellar masses in the range 4.5 − 5.0M�, ii)initial LMC composition (Z = 0.008), iii) assumed very deep dredge-up (λ ∼ 0.9), and iv)inter-shell chemical composition with typically (Xcsh(12C) = 0.02 − 0.03, Xcsh(16O) =0.002 − 0.003, Xcsh(4He) = 0.967 − 0.978). These models experience also HBB (moreefficient at larger masses) as we see by considering the mirror-like evolution of the C- andN-curves in the top-left and top-right panels, respectively. The final points, which would cor-respond to the predicted PN abundances, are clearly in very good agreement with the observeddata for the most He-rich PNe. In particular, models are able to reach He/H∼ 0.17 − 0.20,without over-producing nitrogen, and accounting for the extent of carbon depletion. We notethat the rising part of the C-curves towards the end of the evolution, and the concomitant flat-tening of the N-curves reflect the eventual extinction of HBB while the last dredge-up events


still take place.

Constraints from neon abundances

Within the lowest extension of the error-bars, the data for the most He-rich PNe do not showa significant overabundance with respect to solar, though some increasing trend of Ne/H withHe/H might be present. Some useful indications can be derived.

Recalling that both the first and second dredge-up episodes are expected not to alterthe initial neon abundance, and looking at Fig. 5.5 we point out two facts, namely: i) thepredicted Ne/H after the second dredge-up in the most massive stars (with M ∼ 4 − 5M�)with initial solar composition are already compatible with the measured Ne/H in the mostHe-rich PNe, whereas the models of the same stellar mass but with LMC compositionlie clearly below the observed points; ii) the slightly increasing trend of Ne/H with He/Hat increasing stellar mass merely reflect the decrease in the surface H content due to thedredge-up events, since the neon abundance is completely unaffected.

The consideration of these two points, together with the conclusions from the analysiscarried out in the preceding sections, would point to a significant Ne production havingoccurred in the progenitor stars of the most He-rich PNe, since all other PN abundances(He, C, N, and O) seem globally consistent with stars originating from gas of sub-solarmetallicity. As shown, our intermediate-mass models with LMC composition do satisfy allthese chemical constraints.

Of course, another possibility would be (Ne/Z)LMC > (Ne/Z)�, that is the initialcontent of Ne in the original metal-poor gas was enhanced compared to what is expected fora solar-metallicity-scaled mixture. In this case, there is no necessity that Ne is synthesisedduring the AGB phase.

Going back to the former alternative, which invokes a sizeable Ne production inintermediate-mass stars with LMC composition, we find that models are able to attain a goodagreement with the Ne/H values measured in the most He-rich PNe by assuming that theenrichment of neon is due to the synthesis of 22Ne during thermal pulses via the chain of re-actions 14N(α, γ) 18F(β+, ν) 18O(α, γ) 22Ne. In other words, all nitrogen in the inter-shellshould be converted into 22Ne (see Sect. 5.5.1). The possible channel of subsequent destruc-tion through 22Ne(α, n)25Mg should be inefficient. In our calculations we assume that just1% of the newly synthesised 22Ne is burned into 25Mg (see also Sect. 5.5.1).

Then, in the context of the proposed interpretation, the immediate consequence wouldbe the inefficiency of the 22Ne(α, n)25Mg reaction as production channel of neutrons, withimportant implications for the synthesis of slow-neutron capture elements (Busso et al. 1999).In this case, the major role for the s-process nucleosynthesis would be played by the 13C(α,n)16O channel.

If solar initial metallicity was assumed for these PNe with high helium abundance then,similarly to Sect. 5.6.3, no neon production is needed since the observed values are compati-ble, within uncertainties, to the solar value.


Figure 5.11–. Summary of the results that best fit the observed PN abundances. Specifically, trianglesrepresent the same predictions as in Fig. 5.7, that are derived from TP-AGB models with Z = 0.019and with initial stellar masses from 1.1 to 5.0 M�. The other three symbols correspond to intermediate-mass stars with initial LMC composition (Z = 0.008), namely: pentagon for the 4.5M� model withK) prescriptions, star for the 5.0M� model with K) prescriptions, and diamond for the 5.0M� modelwith J) prescriptions. See text for more details.

5.7. Summary and conclusions 103

Figure 5.12–. The same as in Fig. 5.11, but expressing the abundance data with different combinationsof elemental ratios.

5.7 Summary and conclusionsIn this study a sample of PNe with accurately determined elemental abundances, is usedto derive interesting information about the evolution of the stellar progenitors, and setconstraints on the nucleosynthesis and mixing processes characterising their previousevolution. To this aim, synthetic TP-AGB models are calculated to reproduce the data byvarying the parameters: initial stellar mass and metallicity, molecular opacities, dredge-upand HBB efficiency, and chemical composition of the convective inter-shell developed atthermal pulses.

The clear segregation of the abundance data in two sub-samples, particularly evident inthe O/H – He/H diagram, has led us to discuss them separately. And indeed, our investigationsuggests two different interpretative scenarios. The final results that best reproduce theobserved data are summarised in Figs. 5.11 and 5.12.

From the analysis of the group of PNe with low He content (He/H< 0.15) and solar-likeoxygen abundances, we conclude that:

• The stellar progenitors are low- and intermediate-mass stars with original solar-likechemical composition and initial masses spanning the range 0.9 − 4.0M�.

• The oxygen abundances are consistent with the recent determination for the Sun byAllende Prieto et al. (2001), that is lower than previous estimates (see e.g. Anders


& Grevesse 1989) by almost 0.2 dex. For a few PNe there may be a limited oxygenenrichment, possibly associated with dredge-up during the TP-AGB phase.

• There is clear evidence of carbon enrichment in some PNe that also exhibit C/O> 1,suggesting that they evolved from carbon stars experiencing the third dredge-up duringthe TP-AGB phase.

• Measured carbon abundances are well reproduced by TP-AGB models with dredge-up efficiencies λ ∼ 0.3 − 0.4, and adopting variable molecular opacities in place ofthe usual solar-scaled opacity tables (see Marigo 2002). The introduction of variableopacities prevents the likely over-enrichment of carbon by shortening the duration ofthe carbon-star phase, and causing an earlier shut-down of the third dredge-up due tothe cooling of the envelope structure (Marigo 2003).

• The degree of nitrogen enrichment is consistent with the expectations from the first andsecond dredge-up events, occurred prior to the TP-AGB phase. The efficiency of HBBin intermediate-mass stars with solar-metallicity should be modest.

• Helium abundances are well accounted for by considering the whole contribution of alldredge-up processes (i.e. first, and possibly second and third).

From the study of the extremely helium-rich (0.15 ≤He/H≤ 0.20) and oxygen-poor PNewe can conclude the following:

• The stellar progenitors should be intermediate-mass stars (4−5M�) experiencing boththe third dredge-up and HBB during their TP-AGB evolution.

• The PN oxygen abundances are consistent with a sub-solar initial stellar metallicity.In fact, under the hypothesis of solar metallicity we are forced to invoke a significantoxygen destruction via very efficient HBB, which violates other chemical constraints,e.g. causing a large over-production of nitrogen. Instead, models with assumed initialLMC composition provide a fairly good agreement with the data.

• The first two assumptions are needed in the models to reproduce the observed abun-dances. This leads to a controversy which is important to point out. The combinationof low metallicity with intermediate-mass progenitors is peculiar, since these stars areprobably recently formed from gas with interstellar abundances. Although there areseveral indications that these PNe are of lower metallicity (see Sec. 5.6.4), this couldalso suggest that perhaps another physical process has not fully been taken into ac-count. This issue should be further investigated.

• The long-standing problem – initially formulated by Becker & Iben (1980) – of ac-counting, simultaneously and quantitatively, for the observed N/O–He/H correlationand the C/O–N/O anti-correlation seems to be solved by assuming that the third dredge-up i) is very efficient, and ii) brings up to the surface material containing only a smallamount of primary carbon synthesised during thermal pulses. A good agreement withthe observed data is obtained by adopting λ ∼ 0.9 and Xcsh(12C) ∼ 0.02 − 0.03.

The former indication on the dredge-up efficiency, derived empirically, is supported ontheoretical grounds by full TP-AGB calculations of intermediate-mass stars, i.e. Vas-siliadis & Wood (1993), and more recently Frost et al. (1998) and Siess et al. (2002).

5.7. Summary and conclusions 105

A significant part of the helium enrichment of these PNe should be ascribed to a largenumber of deep dredge-up events that precede the occurrence of the so-called “de-generate pulses”, according to the designation introduced by Frost et al. (1998). Theadditional requirement emerging from our study – that such dredge-up events shouldnot only be extremely deep but also carry a small amount of carbon – is not fully con-firmed by theoretical analyses (i.e. Frost et al. 1998), though a positive indication inthis sense is given by the work of Vassiliadis & Wood (1993).

• A significant production of 22Ne – via α-captures starting from 14N – should takeplace in these stars to reproduce the observed Ne/H values of the He-rich PNe, underthe hypothesis they descend from intermediate-mass stars with initial LMC chemicalcomposition. As direct consequence, this would imply a reduced role of the 22Ne(α,n)25Mg reaction in providing neutrons for the slow-neutron capture nucleosyntesis thatis expected to occur during thermal pulses.

We also note that the invoked inefficiency of the 22Ne(α, n)25Mg channel seems con-sistent with the expected low synthesis of carbon at thermal pulses in the most massiveAGB stars experiencing very deep dredge-up (see former point). In fact, as reported byVassiliadis & Wood (1993) the deep dredge-up quickly extinguishes the helium burningshell. As a consequence this could prevent both a significant production of carbon viathe triple-α reaction and the attainment of the high temperatures required for the fullactivation of the 22Ne(α, n)25Mg reaction. The confirmation of this two-fold aspectdeserves detailed calculations of thermal pulses.

Acknowledgements

P.M. acknowledges the SRON National Institute for Space Research (Groningen) for hospitality andfinancial support during her visit in October 2001, and the Italian Ministry of Education, University andResearch (MIUR) for the work carried out at the Astronomy Department in Padova. J. Bernard-Salasthanks Annette Ferguson for valuable discussions and suggestions as well as the Universita di Padovafor hospitality. We are grateful to Dr. John Lattanzio for the careful reading of this manuscript, and forproviding comments and suggestions that result in an improvement of the paper.

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Probing AGB nucleosynthesis via accurate Planetary Nebula ... · 70 CHAPTER 5: Probing AGB nucleosynthesis via accurate Planetary Nebula abundances 5.1 Introduction Planetary Nebulae